Verfügbarkeit: Denumerable Markov chains | Technische Universität München

Denumerable Markov chains: generating functions, boundary theory, random walks on trees

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Bibliographische Detailangaben
Beteilige Person:	Woess, Wolfgang 1954- (VerfasserIn)
Format:	Buch
Sprache:	Englisch Italienisch
Veröffentlicht:	Zürich Europ. Math. Soc. 2009
Schriftenreihe:	EMS textbooks in mathematics
Schlagwörter:	Boundary value problems Generating functions Markov processes Measure theory Random walks (Mathematics) Markov-Kette Potenzialtheorie Martin-Rand Baum > Mathematik Irrfahrtsproblem
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018012749&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XVII, 351 S. graph. Darst.
ISBN:	9783037190715 303719071X

Internformat

MARC


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Datensatz im Suchindex

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adam_text	Contents Preface v Introduction ix Summary .... ...... . . . . . . . .... . . . .... ... ix Raison d’etre .................................... xiii 1 Preliminaries and basic facts 1 A Preliminaries, examples ............. . . . .... . ... 1 B Axiomatic definition of a Markov chain ........................ 5 C Transition probabilities in n steps......................... 12 D Generating functions of transition probabilities.......... 17 2 Irreducible classes 28 A Irreducible and essential classes . . . .. . . . . ........ . 28 B The period of an irreducible class......... 35 C The spectral radius of an irreducible class .............. 39 3 Recurrence and transience, convergence, and the ergodic theorem 43 A Recurrent classes ......................................... . 43 B Return times, positive recurrence, and stationary probability measures 47 C The convergence theorem for finite Markov chains ......... 52 D The Perron-Frobenius theorem .................................... 57 E The convergence theorem for positive recurrent Markov chains ... 63 F The ergodic theorem for positive recurrent Markov chains ...... 68 G p-recurrence . . .... ... .... ..... . ..... ...... 74 4 Reversible Markov chains 78 A The network model....................................... ... 78 B Speed of convergence of finite reversible Markov chains ...... 83 C The Poincare inequality........................................... 93 D Recurrence of infinite networks........... 102 E Random walks on integer lattices............................... . 109 5 Models of population evolution 116 A Birth-and-death Markov chains........... . ..................116 B The Galton-Watson process ................................ 131 C Branching Markov chains ....................... 140 viii Contents 6 Elements of the potential theory of transient Markov chains 153 A Motivation. The finite case .................................. 153 B Harmonic and superharmonic functions. Invariant and excessive measures .................................................... 158 C Induced Markov chains.......................................... 164 D Potentials, Riesz decomposition, approximation ................ 169 E “Balayage” and domination principle.......... . ...............173 7 The Martin boundary of transient Markov chains 179 A Minimal harmonic functions ......................................179 B The Martin compactification..................................... 184 C Supermartingales, superharmonic functions, and excessive measures 191 D The Poisson-Martin integral representation theorem . ............200 E Poisson boundary. Alternative approach to the integral representation 209 8 Minimal harmonic functions on Euclidean lattices 219 9 Nearest neighbour random walks on trees 226 A Basic facts and computations................................... 226 B The geometric boundary of an infinite tree . ... . . ... ..... 232 C Convergence to ends and identification of the Martin boundary ... 237 D The integral representation of all harmonic functions . ... . . . . 246 E Limits of harmonic functions at the boundary . . . ........... . 251 F The boundary process, and the deviation from the limit geodesic . . 263 G Some recurrence / transience criteria ......................... 267 H Rate of escape and spectral radius .................. 279 Solutions of all exercises 297 Bibliography 339 A Textbooks and other general references.......................... 339 B Research-specific references................................... 341 List of symbols and notation 345 Index 349
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indexdate	2024-12-20T13:49:31Z
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isbn	9783037190715 303719071X
language	English Italian
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-018012749
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physical	XVII, 351 S. graph. Darst.
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spellingShingle	Woess, Wolfgang 1954- Denumerable Markov chains generating functions, boundary theory, random walks on trees Boundary value problems Generating functions Markov processes Measure theory Random walks (Mathematics) Markov-Kette (DE-588)4037612-6 gnd Potenzialtheorie (DE-588)4046939-6 gnd Martin-Rand (DE-588)4451181-4 gnd Baum Mathematik (DE-588)4004849-4 gnd Irrfahrtsproblem (DE-588)4162442-7 gnd
subject_GND	(DE-588)4037612-6 (DE-588)4046939-6 (DE-588)4451181-4 (DE-588)4004849-4 (DE-588)4162442-7
title	Denumerable Markov chains generating functions, boundary theory, random walks on trees
title_auth	Denumerable Markov chains generating functions, boundary theory, random walks on trees
title_exact_search	Denumerable Markov chains generating functions, boundary theory, random walks on trees
title_full	Denumerable Markov chains generating functions, boundary theory, random walks on trees Wolfgang Woess
title_fullStr	Denumerable Markov chains generating functions, boundary theory, random walks on trees Wolfgang Woess
title_full_unstemmed	Denumerable Markov chains generating functions, boundary theory, random walks on trees Wolfgang Woess
title_short	Denumerable Markov chains
title_sort	denumerable markov chains generating functions boundary theory random walks on trees
title_sub	generating functions, boundary theory, random walks on trees
topic	Boundary value problems Generating functions Markov processes Measure theory Random walks (Mathematics) Markov-Kette (DE-588)4037612-6 gnd Potenzialtheorie (DE-588)4046939-6 gnd Martin-Rand (DE-588)4451181-4 gnd Baum Mathematik (DE-588)4004849-4 gnd Irrfahrtsproblem (DE-588)4162442-7 gnd
topic_facet	Boundary value problems Generating functions Markov processes Measure theory Random walks (Mathematics) Markov-Kette Potenzialtheorie Martin-Rand Baum Mathematik Irrfahrtsproblem
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018012749&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT woesswolfgang denumerablemarkovchainsgeneratingfunctionsboundarytheoryrandomwalksontrees

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